Analogs of Gröbner bases in polynomial rings over a ring

Journal of Symbolic Computation

Volumn 21, Issue 2, 1996, Pages 139-153

  Miller, J Lyn ^a  

^a WESTERN KENTUCKY UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030075222     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1996.0006     Document Type: Article

References (16)

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2. Becker, T., Weispfennig, V. (1993). Gröbner Bases: A Computational Approach to Commutative Algebra. Springer-Verlag, New York.
3. Buchberger, B. (1965). Ein Algorithmus zum Auffinden der Basiselemente des Restklassenrings nach einem nulldimensionalen Polynomideal. PhD. Thesis, Inst. University of Innsbruck, Innsbruck, Austria.
4. Buchberger, B. (1985). Gröbner Bases: An algorithmic method in polynomial ideal theory. Multidimensional Systems Theory (N.K. Bose, ed.), Reidel, Dordrecht, 184-232.
5. Cox, D., Little, J., O'Shea, D. (1992). Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer-Verlag, New York.
6. Dachsel, T. (1990). Ein Vervollständigungsverfahren zur Berechnung kanonischer Basen für unitäre Unterringe von Polynomringen. Diplomarbeit, Universität Kaiserslautern.
7. Kapur, D., Madlener, K. (1989). A Completion Procedure for Computing a Canonical Basis for a k-Subalgebra. Computers and Mathematics, Springer, New York, 1-11.
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9. Möller, H.M. (1989). On the construction of Gröbner bases using syzygies. Computational Aspects of Commutative Algebra (L. Robbiano, ed.), Academic Press, San Diego, 211-225.
10. Nakos, G., Glinos, N. (1994). Computing Gröbner Bases over Z. To appear. United States Naval Academy, Annapolis, MD.
11. Ollivier, F. (1990). Canonical bases: relations with standard bases, finiteness conditions and application to tame automorphisms. Effective Methods in Algebraic Geometry (T. Mora and C. Traverso, eds.), Birkhauser, Boston, 379-400.
12. Robbiano, L. (1986). On the Theory of Graded Structures. Journal of Symbolic Computation 2, 139-170.
13. Robbiano, L., Sweedler, M. (1988). Subalgebra Bases. Proc. Commutative Algebra Salvador (W. Burns and A. Simis, eds.), Springer LNM 1430, 61-87.
14. Sweedler, M. (1988). Ideal bases and valuation rings. Manuscript. Cornell University, Ithaca, NY.
15. Trinks, W. (1978). Über Buchbergers Verfahren, Systeme algebraischer Gleichungen zu lösen. J. Number Th. 10/4, 475-488.
16. Zacharias, G. (1978). Generalized Gröbner bases in commutative polynomial rings. Bachelor's Thesis, MIT, Cambridge, MA.